Solve 77-1023 f^4

Question

Factor the expression

11 (7 - 93 f^{4})

Evaluate

77 - 1023 f^{4}

Solution

11 (7 - 93 f^{4})

Show Solution

f_{1} = - \frac{4 7 \times 9 3 ^{3}}{93}, f_{2} = \frac{4 7 \times 9 3 ^{3}}{93}

Alternative Form

f_{1} \approx - 0.523786, f_{2} \approx 0.523786

Evaluate

77 - 1023 f^{4}

To find the roots of the expression,set the expression equal to 0

77 - 1023 f^{4} = 0

Move the constant to the right-hand side and change its sign

- 1023 f^{4} = 0 - 77

Removing 0 doesn't change the value,so remove it from the expression

- 1023 f^{4} = - 77

Change the signs on both sides of the equation

1023 f^{4} = 77

Divide both sides

\frac{1023 f ^{4}}{1023} = \frac{77}{1023}

Divide the numbers

f^{4} = \frac{77}{1023}

Cancel out the common factor 11

f^{4} = \frac{7}{93}

Take the root of both sides of the equation and remember to use both positive and negative roots

f = \pm 4 \frac{7}{93}

Simplify the expression

More Steps

Evaluate

4 \frac{7}{93}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 7}{4 93}

Multiply by the Conjugate

\frac{4 7 \times 4 9 3 ^{3}}{4 93 \times 4 9 3 ^{3}}

The product of roots with the same index is equal to the root of the product

\frac{4 7 \times 9 3 ^{3}}{4 93 \times 4 9 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

493 \times 4 9 3^{3}

The product of roots with the same index is equal to the root of the product

4 93 \times 9 3^{3}

Calculate the product

4 9 3^{4}

Reduce the index of the radical and exponent with 4

93

\frac{4 7 \times 9 3 ^{3}}{93}

f = \pm \frac{4 7 \times 9 3 ^{3}}{93}

Separate the equation into 2 possible cases

f = \frac{4 7 \times 9 3 ^{3}}{93} f = - \frac{4 7 \times 9 3 ^{3}}{93}

Solution

f_{1} = - \frac{4 7 \times 9 3 ^{3}}{93}, f_{2} = \frac{4 7 \times 9 3 ^{3}}{93}

Alternative Form

f_{1} \approx - 0.523786, f_{2} \approx 0.523786

Show Solution